The Bloomberg administration and the City Council are getting down to the wire negotiating the city’s next fiscal year budget, but are expected to have a handshake agreement today or tomorrow.

Senior finance staff from both sides of City Hall spent most of yesterday in closed-door meetings, negotiating how much money the city should spend on everything from libraries to tree pruning.

The portion they are haggling over – between $200 million and $300 million, depending on their agreement – is just a small sliver of the roughly $50 billion budget. Sources said late yesterday afternoon that the two sides settled on $250 million to restore programs that were funded last year but not included in the mayor’s latest budget proposal.

Mayor Bloomberg’s willingness to give in could deny the speaker of the council, Gifford Miller, and the three other Democrats vying for the party nomination to run against Mr. Bloomberg, a campaign issue in the coming months.

Until late yesterday afternoon, when Mr. Miller’s office phoned the 48 Democratic council members to notify them that a majority caucus would meet this morning, many members and their usually well-informed staffers were in the dark about the status of the budget talks.

“We’re certainly down to the wire, but there must be discussions going on, otherwise we wouldn’t be called in for meetings,” said Council Member Gale Brewer, a Democrat who represents the Upper West Side.

Yet by last night, some council members were confident that a deal would be made today, which would give them extra time before the scheduled vote on Thursday to figure out how much they would be able to dole out to organizations in their districts.

Meanwhile, lobbyists spent yesterday making final cases for the organizations they represent.

The Dryfoos Group, a lobbying firm that netted nearly $730,000 from clients last year, circulated a clear binder containing about 100 pages outlining its budget requests.

The requests included roughly $18.1 million in spending for organizations ranging from the American Folk Art Museum to the New York Junior Tennis League, and approximately $20.4 million for capital projects for those groups.

A former council member who is now a lobbyist, Robert Dryfoos, said the organizations he represents provide “blue-chip services” to residents throughout the city. He called himself an “unabashed advocate.”

Though Mr. Miller may have to hold his nose to come to an agreement with a mayor he is trying to unseat, the budget is rosier than it was last year.

Two last-minute issues that are being factored in are a pending decision to increase the salaries of police officers, and a rollback on the city’s sales tax on clothing.

“Look, we have come to an on-time budget, and the speaker and I have shaken hands in the rotunda of City Hall three times in a row,” Mr. Bloomberg told reporters. “And there’s absolutely no reason not to think that we’re not going to have another on-time budget, and the speaker and I will be there, shaking hands again.”